Question

A dealer sold two TV sets for Rs 2,400 each, gaining 20% on one set and losing 20% on the other set. Find his net gain or loss and also express it as a percentage.

A.Loss = Rs 120, loss % = 1%
B.Loss = Rs 150, loss % = 2%
C.Loss = Rs 190, loss % = 3%
D.Loss = Rs 200, loss % = 4%

Answer 1

Hint- Here, in this question, two items have been sold by the shopkeeper with the same SP but different CPs, so we need to calculate the net gain or loss and consequently the gain or loss per cent. We need to apply the formula for the profit per cent and the loss per cent respectively for the two different cases.


Complete step by step solution:
For the first TV, substitute SP = Rs 2,400 and profit = 20% in the formula \[{\text{Profit}}\% = \dfrac{{SP - CP}}{{CP}} \times 100\] to determine the cost price for the shopkeeper for the first TV as:

$
  20 = \dfrac{{2400 - C{P_1}}}{{C{P_1}}} \times 100 \\
  2400 - C{P_1} = 0.20C{P_1} \\
  1.20C{P_1} = 2400 \\
  C{P_1} = \dfrac{{2400}}{{1.20}} \\
   = 2000 \\
 $
Now, for the second TV, substitute SP = Rs 2,400 and loss = 20% in the formula ${\text{Loss\% }} = \dfrac{{CP - SP}}{{CP}} \times 100$ to determine the cost price for the shopkeeper for the second TV as:

$
  20 = \dfrac{{C{P_2} - 2400}}{{C{P_2}}} \times 100 \\
  C{P_2} - 2400 = 0.20C{P_2} \\
  0.8C{P_2} = 2400 \\
  C{P_2} = \dfrac{{2400}}{{0.8}} \\
   = 3000 \\
 $

The total cost price of both TVs is:
$
  CP = C{P_1} + C{P_2} \\
   = 2000 + 3000 \\
   = 5000 \\
 $

Also, Total SP is calculated as:
\[
  \;SP = S{P_1} + S{P_2} \\
   = 2400 + 2400 \\
   = 4800 \\
 \]

Since Total SP is smaller than the total CP, there will be a loss which is calculated as:
$
  Loss = CP - SP \\
   = 5000 - 4800 \\
   = 200 \\
 $
Now, substitute $CP = 5000{\text{ and }}SP = 5000$ in the formula $Loss\% = \dfrac{{CP - SP}}{{CP}} \times 100$ to determine the loss per cent to the shopkeeper as:

$
  Loss% = \dfrac{{5000 - 4800}}{{5000}} \times 100 \\
   = 4\% \\
 $

Hence, the net loss is Rs 200, and the loss % is 4%.
Option (D) is correct.


Additional Information: When a product is purchased in the view of selling it to the consumer in order to do business then, the price in which the product is bought by the seller is known as the cost price of the product and the price in which the seller sells the product to the consumer is known as selling of the product for the seller. If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product.

Note: It is always to be kept in mind that the profit or loss percent of a product is always calculated on the cost price of the product and not on the selling price. Moreover, students often confuse the marked price and the selling price of the product, these two terms are different. Marked price is the price fixed by the seller before discount but selling price is the price in which the product is actually sold.